With the current three-dimensional cone beam reconstruction with the aid of C-arm systems, the so-called Wide Object Problem arises during the examination of certain body regions (such as for instance abdomen or breast), which exceed a maximum width determined by the recording geometry (detector dimension and focal length). A decisive processing step for 3D reconstruction using filtered back projection is the filtering of the projection data along lines, which run horizontally or approximately horizontally in the detector.
As a result of the non-local nature of the filter core (such as ramp filters or Hilbert filters for instance), the filter lines must pass through the whole projection of the examination area and may not herewith be truncated, even if only one part of the region of interest (ROI) is to be reconstructed. In many recordings, the limited detector width however results in transaxially truncated projections of the region of interest, since this cannot be completely covered by the field of view (FoV). The said field of view results in truncated filter lines in these projections. The results are significant reconstruction artifacts, such as for instance so-called truncation artifacts, which distort the result and hinder, complicate or render impossible the qualified diagnosis thereof.
The so-called Wide Object Problem relates to almost all current reconstruction algorithms, which operate on the basis of filtered back projection (FBP algorithms), and that is the vast majority. This applies in particular to the Feldkamp algorithm, which is designed for a circular scanning path of the focal point and is known from L. A. Feldkamp, L. C. Davis, J. W. Kress: Practical Cone-Beam Algorithm, J. Opt. Soc. Am. A, Vol. 1, No. 6, pages 612-619. More recent precise reconstruction methods (such as for instance known from A. Katsevich: “Image Reconstruction for the Circle and Arc Trajectory”, Physics in Medicine and Biology, Vol. 50, pages 2249-2265, April 2005 and from J. Pack, F. Noo: “Cone-Beam Reconstruction Using ID Filtering Along the Projection of M-Lines”, Inverse Problems, Vol. 21, pages 1105-1120, April 2005) require extended path curves for scanning (such as circle and line, circle and circle arc), but nevertheless feature this problem. A stable solution for the Wide Object Problem would thus constitute an important and central contribution to solving reconstruction problems in computed tomography.
Back projection filtration (BPF) methods, which only implement filtering in the object space following back projection and only allow local calculation steps on the projection data, can cope with truncated projections up to a certain degree. This has been demonstrated using the example of a helix-shaped (J. Pack, F. Noo, R. Clackdoyle: “Cone Beam Reconstruction Using the Back projection of Locally Filtered Projections” IEEE Transactions on Medical Imaging, Vol. 24, No. 1, pages 70-85, January 2005; E. Y. Sidky, Y. Zou, X. Pan: “Minimum Data Image Reconstruction Algorithms with Shift-Invariant Filtering for Helical, Cone-Beam CT” Physics in Medicine and Biology, Vol. 50, pages 1643-1657, 2005) and a circular (L. Yu, D. Xia, Y. Zou, X. Pan, C. Pelizzari, P. Munro: “Region of Interest Reconstruction from Truncated Data in Circular Cone-Beam CT”, Proceedings of the SPIE, Vol. 5747, pages 412-418, 2005) path curve for scanning for cone beam reconstruction. In some instances, the BPF approach solves the problem of truncated projections and enables an artifact-free reconstruction of an ROI within the examination area.
Furthermore, a FBP method derived from the BPF approach is known (E. Y. Sidky, Y. Zou, X-Pan: “A Minimum Data FBP-Type Algorithm for Image Reconstruction in Cone-Beam CT”, Eighth International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine, Salt Lake City, Utah, Jul. 6-9, 2005), which comprises similar characteristics. The region of interest is however limited to the field of view (FoV), so that even with this method, it is frequently not possible to reconstruct the complete region of interest (such as for instance abdomen of a large patient).
Methods also exist however, which enlarge the field of view (FoV). By way of example, reference is made here to the detector displacement method, in which the detector is no longer arranged symmetrically in respect of the optical axis, but instead with a certain displacement (V. Liu, N. R. Lariviere, G. Wang: “X-ray Micro-CT with a Displaced Detector Array: Application to helical cone-beam reconstruction”, Medical Physics, Vol. 30, No. 10, pages 2758-2761, October 2003). The detector displacement method however requires a circular or helical path curve for scanning over an angular range of at least 360 degrees. Furthermore, with cone-beam geometry, this method represents an approximate field of view (FoV) enlargement and thus results in artifacts in the event of large cone angles.
A similar approach is the extrapolation of truncated projection data. In P. S. Cho, A. D. Rudd, R. H. Johnson, “Cone-Beam CT from Width-Truncated Projections”, Computerized Medical Imaging and Graphics, Vol. 20, No. 1, pages 49-57. 1996) the missing line integrals are expanded based on approximate assumptions (such as for instance the quasi redundancy of opposite beams, with the cone angle being ignored). This method also requires a path curve of 360° for scanning. In particular, the last-mentioned method is understood as an extension of the FDK algorithm.